One of the key men behind the result was Darwin Nunez who came off the bench and produced an impressive cameo in the final 30 minutes.
The 23-year-old Uruguay international, who became the club's record signing at £85million, won a late penalty which was converted by Mo Salah before heading home Liverpool's third goal in stoppage time.
The forward also caused City goalkeeper Ederson a number of problems as he threatened to further improve his team's advantage.
"It was good, it was really good. It is clear it will get better with time," said Klopp.
"We live in a world where everybody gets judged on first sight and that's not helpful for anybody but it happens constantly.
"In the first few games (of pre-season) we were not even close to the fitness level of today and then when he came on, we passed each ball for him to chase it and after the third ball he was completely killed and then everybody judged his first touches and these kind of things.
"It's just a joke but we have to live with that, he will deal with it brilliantly. We are patient and we know he can do good stuff.
"We all know they are a special species, strikers. The other thing everybody needs (are) little positives. That means goals, or goal involvements.
"I think Darwin would have been fine even without scoring the third one because the penalty was Millie's cross and his header.
"The chance he had before he did really well, but Ederson reacted brilliantly. The goal was obviously the icing on the cake, so really pleased for him.
"You could see in his face, you could see in the face of all his team-mates how happy the boys are for him and that's a really good sign after that short period of time that he is with us."